Tenant Screening Issue

[Gerald Barron]

So here's my dilemma and I'm not sure how to handle it. I had a prospective tenant. we will call them Tenant #1, come see one of my units and start the application process. During the credit/background portion, they were locked out of the system because they forgot they froze their credit. Tenant #1 has no problems completing the credit/background once the system is unlocked and I have already verified employment and references so I don't see any red flags per se but they haven't completed the application process. Tenant #1 also negotiated a lower rent than what we had listed. On top of this, they agreed to give us a security deposit to hold the property until they can complete the application. I told her until I receive funds I will continue to show the property. All this was negotiated through text and I have not accepted any funds yet.  

Enter second prospective renter. Today, I had another prospective renter come to see the property just this morning. She loved the place and immediately after leaving filled out the application and completed a credit/background check. From what I can see on the credit report she has a much better debt to income ratio than prospective tenant #1 and a great rental history. She agreed to our full price rental listing and did not try to negotiate the rent down.  I mentioned to here that tenant #1 is also in the application process but had not completed it yet. She said no problem but let her know because she is ready to move in. 

So I guess my biggest concern is whether or not I'm obligated to take Tenant #1 since we agree to terms (nothing signed) but hasn't they completed the application process where Tenant #2 has already completed the application process (and arguably looks better on paper) and has agreed to full price rent?